U.S. patent number 3,774,864 [Application Number 05/163,813] was granted by the patent office on 1973-11-27 for cargo aircraft having increased payload capacity versus weight.
This patent grant is currently assigned to Lockheed Aircraft Corporation. Invention is credited to Charles H. Hurkamp.
United States Patent |
3,774,864 |
Hurkamp |
November 27, 1973 |
CARGO AIRCRAFT HAVING INCREASED PAYLOAD CAPACITY VERSUS WEIGHT
Abstract
An aircraft configuration provides for structural arrangement
whereby large cargo aircraft with appreciably increased pay-load
capacity for a given airframe weight is possible. This
configuration lends itself to the incorporation of optimum lift,
thrust and landing systems. The total result is a large cargo
aircraft capable of competing costwise with surface transportation
modes. This invention relates to cargo type aircraft, and more
particularly to such an aircraft of selected design and
configuration so as to permit the adjustment of its load carrying
capability with respect to its basic weight as well as its lift to
drag to the end that maximum payload capacity can be realized for a
given airframe weight. In an effort to compete with surface
transportation modes from a cost standpoint, cargo aircraft have
grown increasingly larger until they have now reached a point where
further size increases alone no longer result in a net gain, i.e.,
the point of diminishing returns. Thus, a size has been attained
where increased payload capacity requires the addition of
corresponding weight and drag. The ratios of payload to empty
aircraft weight and lift to drag have been extended to a practical
limit by various refinements heretofore made with respect to
materials and structure, as well as by engine performance, i.e.,
thrust or power output. At the same time, use of abnormally large
cargo aircraft aggravates the total operating conditions and
creates new problems therein with respect to aircraft range,
landing and take-off performance (due not only to aircraft
operation, but to runway and terminal requirements) and the like.
These have resulted in such developments, for example, as boundary
layer control, whereby air stagnation on the external surfaces of
the airplane is eliminated by various schemes and devices, such as
by blowing and suction of air to produce a laminar flow over the
upper surface of the wing for drag reduction and over the deflected
trailing edge of the wings to effect lift augmentation. The present
invention comtemplates a totally different approach toward a new
generation of cargo aircraft, wherein by design configuration, a
near uniform distribution of internal loading to match the external
airloads can be obtained. This design further allows for minimized
body structure resulting in improved ratios of both useful load to
gross weight and of lift to drag, with the ability to achieve high
productivity at relatively low costs. More specifically, the
present design arrangement includes a relatively thick (in the
range of 15 to 25 percent of the chord), highlyswept wing of low
aspect ratio (less than about 6) with a substantially constant
airfoil section, preferably contoured so as to delay the onset of
drag rise due to compressible flow and two outer nacelles one at
each remote wing tip to which an empennage assembly is attached.
The wing elements are arranged to provide space for multiple rows
of cargo which can be on-and-off loaded from doors provided
therefor through each nacelle at the wing tips. At their adjacent
or root ends the wing elements include internal passageways so that
the entire swept wing constitutes a continuous cargo compartment
from tip to tip. This arrangement provides the necessary cargo
capacity with a minimum amount of non-lifting structure to effect
substantial savings in weight and drag. If desired, a center body
or nacelle may be employed at the juncture of, i.e., between, the
wing elements, and in this case, additional space is provided with
greater width and head room available for outsized cargo. Also this
center nacelle used in conjunction with the two outer nacelles may
serve as a base structure for a three-element type of landing gear,
which may be comprised of aircushion trunks one associated with the
undersurface of each nacelle. Propulsion is provided by engines
preferably of the turbo-fan type mounted on the top of the wing
structure and spaced at intervals along the span. This allows for
the turbine exhaust of each engine to be ducted to a fixed nozzle,
while the fan exhaust may be ducted to a diverter valve, permitting
the fan air to be discharged through a separate nozzle for all
operation except take-off and landing. In the latter modes, the fan
air may thus be diverted to a spanwise duct within the wing to
provide a distributed spanwise jet over the flaps and control
surfaces. This action serves to provide augmented lift and control
power in the low-speed flight regimes.
Inventors: |
Hurkamp; Charles H. (Hilton
Head Island, SC) |
Assignee: |
Lockheed Aircraft Corporation
(Burbank, CA)
|
Family
ID: |
22591688 |
Appl.
No.: |
05/163,813 |
Filed: |
July 19, 1971 |
Current U.S.
Class: |
244/13; 244/36;
244/207; 244/123.9 |
Current CPC
Class: |
B64C
39/10 (20130101) |
Current International
Class: |
B64C
39/10 (20060101); B64C 39/00 (20060101); B64c
001/00 (); B64c 003/02 () |
Field of
Search: |
;244/12R,13,15,36,42CC,87,112,117R,118R,118P,119,123,137R,129D
;105/357,361 ;214/84 ;114/.5R |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Primary Examiner: Reger; Duane A.
Assistant Examiner: Sotelo; Jesus D.
Claims
What is claimed is:
1. An aircraft comprising a wing having tip-mounted outer bodies
each terminating aft in an empennage unit consisting of a fixed
vertical surface with a hinged rudder and a fixed horizontal
surface mounted on top of said vertical surface with a hinged
elevator, and a center body located midway between said outer
bodies;
said center body having a generally unobstructed interior
constituting a cargo compartment, an access opening in at least one
end of said center body adapted for on-and-off cargo loading, and a
removable door for each said center body opening;
said wing having a substantially constant chord length, a sweep
back angle, an airfoil section having a thickness to chord ratio in
the range of 15 -25 percent, an internal structure defined by the
external aircraft skin and comprising at least two vertical webs
each extending spanwise and disposed at and along a constant chord
location with the most forward and most rearward webs connected to
ribs extending substantially in a chordwise direction and to said
skin, at least one open cell extending spanwise of said wing
between said outer bodies and bonded by chordwise panels attached
to the inner face of said skin and interrupted centrally to define
an interior height and width corresponding to predetermined size
cargo to be placed therein, an access opening in the wall of each
said outer body remote from the associated wing cell aforesaid
affording entry thereto from the exterior of the aircraft, said
opening having cross-sectional dimensions equal to those of the
adjacent end of said cell and in substantial alignment therewith
for on and off cargo loading, and a removable door adapted to close
each said outerbody opening.
2. The aircraft of claim 1 including spanwise rollers in the
corners of each said cell supported by said chordwise panels and
said vertical spanwise webs to facilitate the movement of said
cargo units thereover after admittance into one of said access
openings.
3. The aircraft of claim 1 wherein said wing further includes a
floor structure supported on said chordwise panels attached to the
adjacent skin with the intervening space between the floor
structure and skin forming a fluid-tight compartment.
4. The aircraft of claim 1 wherein said wing further includes
internal spanwise curved diaphragms capable of resisting
predetermined internal pressures and combining to enclose the open
cargo along the forward, rearward and upward boundaries, the radius
of curvature of each upper diaphragm and that of the remote,
opposite skin portion being greater than that of the forward and
rearward diaphragms, and said webs serve to resist the tension
loads created by internal pressure acting against the adjoining
differently curved diaphragms, a spanwise walkway between each said
web and the associated forward and rearward curved diaphragms to
permit the passage of personnel, and at least one cutout in each
web to permit crossover between said walkways.
5. The aircraft of claim 1 including a plurality of turbine-driven
fan type engines each mounted in a forward position on the upper
surface of said wing, the turbine exhaust and fan exhaust streams
being separately ducted in a rearward direction with the turbine
exhaust duct enclosed in the fan exhaust duct from which it emerges
in a constricted nozzle and the fan exhaust duct terminates in a
constricted nozzle.
6. The aircraft of claim 5 including a spanwise duct for the
passage of compressed air located immediately aft of said cargo
cells and terminating rearwardly in a slot forming a nozzle located
adjacent the upper surface of a hinged flap defining the trailing
edge of said wing, and a pair of diverter valves one located
immediately forward of said fan exhaust nozzle and the other
located in an opening between said rearward fan exhaust duct and
said spanwise duct, said valves being operative to direct the fan
exhaust stream alternatively through said fan exhaust nozzle and
through said slot nozzle.
7. The aircraft of claim 6 wherein said slot nozzle is defined by a
pair of hinged vanes operable to selectively and alternatively
define a rearwardly directed nozzle and a forwardly and upwardly
directed nozzle.
8. The aircraft of claim 7 further including an opening in said
turbine exhaust duct forwardly of its constricted nozzle, a valve
adjacent said exhaust duct nozzle operative to selectively and
alternatively direct turbine exhaust gas through said constricted
nozzle in an aft direction relative to said aircraft and through
said opening in a relatively forward direction.
9. The aircraft of claim 6 further including an extension duct
connected to said spanwise duct at each outer end thereof and
contained within each said fixed vertical and horizontal empennage
surface, each said extension duct being located adjacent the
associated hinged rudder and elevator and terminating in a slot
forming a nozzle located adjacent each external surface of said
associated rudder and elevator, said rudder and said elevator being
formed with a first surface in contact with and overlying so as to
close said slot nozzles on each side thereof when disposed in its
neutral position and a second surface in spaced relation to a slot
nozzle on one side only thereof when displaced from its neutral
position.
10. The aircraft of claim 6 further including an extension duct
connected to said spanwise duct at each outer end thereof and
contained within each said fixed vertical and horizontal empennage
surface, a portion of each said extension duct within each said
horizontal empennage surface being located immediately forward of
the associated hinged elevator and incorporating a continuous slot
forming a nozzle located adjacent each external surface of said
associated elevator designed and adapted to discharge exhaust air
along only one of said external elevator surfaces when said
elevator is displaced from its neutral position.
11. The aircraft of claim 6 further including an extension duct
connected to said spanwise duct at each outer end thereof and
contained within each said fixed vertical empennage surface and
located immediately forward of the associated hinged rudder, said
extension duct incorporating a continuous slot forming a nozzle
located adjacent each external surface of said associated rudder
designed and adapted to discharge exhaust air along only one of
said external rudder surfaces when said rudder is displaced from
its neutral position.
12. The aircraft of claim 6 wherein each of said outer bodies and
said center body incorporates an air cushion to support the weight
of said aircraft on adjacent surfaces by creating distributed
reaction pressure acting between the underside of said bodies and
said supporting surfaces, said pressure being provided by the
explusion of compressed air from said engine fan ducts through said
spanwise duct into an inflatable elastomeric trunk having
peripheral holes.
13. The aircraft of claim 6 wherein said sweep back angle is
between 30.degree.-40.degree. beginning at the sides of the center
body and including an incident angle relative to the plane of the
surface supporting the aircraft of between about 3 and 8
percent.
14. The aircraft of claim 13 wherein said wing has substantially
zero dihedral and no significant taper.
15. The aircraft of claim 1 wherein three vertical webs are
employed located at 20, 40, and 60 percent, respectively, of the
chord.
16. The aircraft of claim 6 further including an attachment of
continuous elastic fabric secured at and along the outermost edge
defining the planform of said wing and at and along the
undersurface of said wing inwardly of and substantially parallel to
said planform edge, and duct means between said spanwise duct and
the portion of said wing underlying said attachment.
Description
With the above and other objects in view, as will be apparent, this
invention consists in the construction, combination and arrangement
of parts all as hereinafter more fully described, claimed and
illustrated in the accompanying drawings, wherein:
FIG. 1 is a plan view of a cargo aircraft designed and constructed
in accordance with the teachings hereof to show generally the
sweptback wings and the relationship thereof with the outer
nacelles and their respective empennage assemblies, a center
nacelle being employed at the adjacent or root ends of the
wings;
FIG. 2 is a section taken along line 2--2 of FIG. 1 to show
primarily the wing structure normal to the spanwise elements and
the internal arrangement thereof defining the cargo compartments
together with the relationship of the wing and its components with
each engine whereby exhaust ducting is accomplished to correspond
to different flight regimes of the aircraft;
FIG. 3 is a section taken along line 3--3 of FIG. 1 to show the
longitudinal structure of the centerbody or nacelle including the
end closures for openings therein to permit on-and-off cargo
loading of the storage compartment or hold including an associated
air cushion trunk, constituting one element of the landing gear
system, the open position of the end closures being illustrated in
phantom lines;
FIG. 4 is a section taken along line 4--4 of FIG. 1 to show the
transverse structure of each outer nacelle and the construction and
mounting of the associated closure for the end opening therein to
permit on-and-off cargo loading to the primary storage compartment
within each wing, the open position of said closure and the
inflated condition of an air cushion landing gear trunk associated
therewith being illustrated in phantom lines;
FIG. 5 is a section taken along line 5--5 of FIG. 1 to show
generally the chordwise wing structure adjacent the outer nacelle
and empennage relationship therewith as well as the associated
portion of the landing gear trunk in the inflated condition;
FIG. 6 is a section taken along line 6--6 of FIG. 3 to show the
transverse structure of the center nacelle and passage of the
spanwise wing ducts therethrough for the uninterrupted flow of fan
air from the engines on one side of the center nacelle to the other
side;
FIG. 7 is a section taken along line 7--7 of FIG. 2 to show the
details of construction of one of the spanwise vertical tension
members between the upper and lower wing skins;
FIG. 8 is a section taken along line 8--8 of FIG. 5 to show the
transverse structure of the vertical stabilizer of the empennage,
being for all intents and purposes the equivalent of the transverse
structure of the horizontal stabilizer;
FIG. 9 is a plan view of one symmetrical half of the center nacelle
and associated wing portion to show a modified structure thereof to
include an elastic fabric attachment adjacent the leading and
trailing edge portions of the wings constituting a combination
variable airfoil profile means and air cushion landing system;
FIG. 10 is a chordwise cross-section taken through the wing shown
in FIG. 9 to show the attachment in the fully inflated condition
corresponding to landing and take-off operation and an associated
surface whereby a cushion of air is contained within the area
defined by the attachment or trunk to support the aircraft;
FIG. 11 is a section similar to FIG. 4 to show the outer wing tip
of the aircraft with the attachment of FIGS. 9 and 10 thereon and
in the fully inflated condition of FIG. 10; and
FIG. 12 is a section taken along line 12--12 of FIG. 2 to show the
installation of a typical flanged roller as may be positioned along
the four corner intersections of each cargo compartment to support
cargo containers of standardized dimensions.
Referring more particularly to the drawings, 10 designates a cargo
type aircraft having a generally cylindrical center body or nacelle
11 with openings 12 and 13 at opposite ends and a generally
unobstructed interior constituting a cargo storage area or
compartment 14. Appropriate closures 15 and 16, respectively, are
mounted following conventional practice at each end of the nacelle
11 for movement to and from positions uncovering the associated
openings 12 and 13 to permit cargo on and off loading and overlying
and enclosing the openings 12 and 13 whereby to form
aerodynamically clean continuations of the external surface of the
nacelle 11 during flight operations of the aircraft. A pilot's
compartment or cabin 17 is provided in the forward end and at the
top of the nacelle 11.
Extending from each side of the nacelle 11 is a wing 18 which
terminates at its outer end in a generally oblong outerbody or
nacelle 19 which is generally circular in section. Each outer
nacelle 19 is formed with a nose that extends forwardly of the
leading edge 20 of the associated wing 18 and terminates in an aft
extremity 21 that is substantially adjacent the trailing edge 22 of
the wing 18. An upswept empennage assembly 23 extends from the aft
extremity 21 and includes a vertical stabilizer 24 topped by a
horizontal stabilizer 25 forming a so-called "T-tail." Since each
wing 18 and outer nacelle 19 including its empennage assembly 23 is
identical, further description herein to one such half of the
aircraft 10 is to be understood as applicable to the other
symmetrical half of the aircraft 10 as well.
Mounted on each wing 18 is an appropriate number of engines 26. By
way of example, six turbofan engines 26 are illustrated, three
being mounted on top of each wing 18 with their inlet ducts
adjacent the leading edge 20 of the wing 18. Spanwise engine
spacing is consistent with uniform weight and thrust distribution.
The hot turbine exhaust from each engine 26 is separately ducted as
at 28 through a primary nozzle 29, while the relatively cool fan
exhaust air is ducted as at 30 to a plenum 31. A pair of diverter
valves 32 and 33 are mounted adjacent the aft end of the plenum 31.
In the higher speed flight modes, valve 32 is closed and valve 33
opened whereby the fan air flows straight back through a circular
fixed area nozzle 34. In the low speed flight mode valve 33 is
closed and valve 32 opened so that all of the fan air flows into a
spanwise duct 35 from which it emerges through a continuous slot 36
as a thrust-producing boundary layer control jet.
The effective size of this slot 36 is controllable by a spanwise,
narrow chord, two-element vane 37 above the wing flap 38. The rear
element 39 of this vane 37 regulates the effective nozzle area to
an optimum amount for the number of engines 26 in operation while
the forward element 40 functions as a thrust reverser. Since the
duct 35 is connected across the center nacelle 11 (FIG. 6), the
effective area of the slot 36 can be differentially regulated to
provide lateral and directional trim for unsymmetrical engine
thrust or to augment roll control moments.
The forward element 40 of the control vane 37 is normally closed.
It is opened when reverse thrust is desired for the landing run, at
which time the rear element 39 is closed. When the forward nozzle
element 40 is opened, the rear nozzle element 39 is concurrently
closed and vice versa, this being accomplished by any conventional
means per se of no importance to the present invention. It is
contemplated that this type of thrust reverser will provide about
60 percent reverse thrust without the likelihood of inlet
temperature rise.
A similar type of reverser in the form of a butterfly valve 41 is
incorporated forward of the primary nozzle 29. To this end the
upper wall of the duct 28 is cut out and a centrally hinged vane 42
sized to fill such cutout is mounted therein on a pivot 43. This
vane 42 is configured to substantially conform to the transverse
size and shape of the duct 28 so that when rotated by suitable
conventional means to a position at substantial right angles to the
duct 28 it blocks the duct passage and thereby closes the nozzle
29. At the same time, the forward position of the duct cutout is
open and the associated and portion of the vane 42 extends
outwardly of the engine wall. In its opposite extreme position, the
vane 42 completely fills the cutout and forms an aerodynamically
clean continuation of the engine and duct walls. In this position
of the vane 42, the nozzle 29 is completely open.
The major portion of the payload and all of the fuel are carried
within the wing 18. To this end, the wing 18 is formed of a
structural box which serves as a receptacle for both items of
useful load. The boundaries of this box are the front and rear
spars in the form of vertical webs 44 and 45 and upper and lower
skin elements 46 and 47. The entire area may be pressurized and
surrounded for this purpose by curved wall panels which include the
highly curved lower skin 47, two arcuate panels or sheets 49 and 50
below the upper skin restrained by a vertical tension member or web
51 and an arcuate sheet 52 and 53 at each of the front and rear
webs 44 and 45, respectively. The latter sheets 52 and 53 provide
spanwise access in the form of walkways 54 for crew or other
on-board personnel for inspection or servicing of the cargo.
Cutouts 48 in the webs 44, 45 and 51 permit crossover between the
walkways 54.
Pressurization of this cargo/fuel area can be accomplished simply
by submitting bleed air from the fan plenums 31 of each engine 26.
This may be accomplished in various ways all well within the known
art, e.g., a series of pressure regulators 55 may be provided at
spaced intervals along the duct 35.
Multiple parallel spanwise compartments 56 for cargo are designed
to accommodate standard size containers. One means of retaining
these containers is to install a row of rollers 57 disposed at
45.degree. angles at each corner so that the loads will be reacted
at structural intersections. By the use of dual parallel
compartments 56 a total of four such compartments can be made
available in the wings 18 and the center nacelle 11 can employ dual
fore and aft rows of containers, for example.
The cargo space or compartments 56 may be specifically sized to
accommodate standard cargo with an entrance door 58 for such cargo
placed in the tip of each wing outer nacelle 19 and, as above
described, with a closure 15 and 16 at the front 12 and/or rear 13
ends of the center nacelle 11. The fuel may be carried within the
cargo floor structural envelope of each wing 18 which for this
purpose is constructed and assembled and, if necessary, sealed in
appropriate conventional manner to make it fluid tight and the ribs
or bulkheads 59 supporting the floor 60 are appropriately pierced
by openings 61. Both the wing cargo and fuel are balanced about 40
percent of the wing chord which is related in position to near the
CG (indicated in FIG. 1) of the aircraft 10. Approximately 80
percent of the useful load is uniformly distributed spanwise from
root to tip of the wings 18 while the remainder is located in the
center nacelle 11.
As stated above, the principal structure of the aircraft 10 is that
of the wings 18 which comprise thick, constant chord airfoils
across the entire span. Each wing 18 has a sweep-back angle on the
order of 30.degree.-40.degree. beginning at the sides of the center
nacelle 11. There is no significant dihedral and no significant
taper and the entire wing 18 has an incident angle within the range
of 3-8 percent, with about 5 percent being preferred, relative to
the supporting surface level indicated at G. The wing 18 may be
constructed of sandwich material preferably with high strength
fiber composite face sheets and either a honeycomb or rigid plastic
form as a core material. The vertical webs 44, 51 and 45 are placed
at approximately 20 percent, 40 percent and 60 percent respectively
of the chord forming the boundaries of the double lobe cargo area
defined by the compartments 56.
The arcuate panels or sheets 52 and 53 constitute pressure
diaphragms located forward of the front web 44 and aft of the rear
web 45 while the panels or sheets 49 and 50 serve a similar
function under the relatively flat upper surface of the wing 18. As
shown in FIG. 2, the sheets 49, 50, 52, and 53 extend spanwise of
the wing 18 coacting with transverse sheets between the adjacent
inner face of the wing skin to form chordwise panels interrupted
centrally to define the compartments 56. While the lower surface of
the wing 18 has sufficient curvature to function as a diaphragm it
is primarily designed to take bending loads and hoop tension. None
of these pressure diaphragms are required to be stiffened as, for
example, with core material. The cargo floor 59, however, is
preferably of sandwich structure designed to take both concentrated
and distributed loads.
The landing gear is preferably of the air cushion type, consisting
of three elements, installed at the center and the two outer
nacelles. Each element is an inflatable elastomeric trunk 62 which
is equipped with peripheral slots or holes 63 for the inward
discharge of air which may be supplied to all of the trunks 62 by
bleed air from the engine fan air distribution ducts 35 in any
suitable manner such as, for example, by conduits 35'. When not in
use, the deflated trunks 62 are stretched tightly against their
supporting bodies 11 and 19. When the trunk 62 is inflated, the
areas A defined by the several peripheral holes 63 under each
nacelle 11 and 19 combine to give a three-point support to the
aircraft 10. At the same time a low-pressure interface is thereby
created with the supporting surface G providing compatibility with
virtually any kind of surface, either terrain or water. The area
defined by the peripheral nozzles or holes 63 is sufficient to
provide adequate buoyancy to float the aircraft 10 in close
proximity to the surface G.
As shown in FIGS. 3, 4, 5, and 6, a trunk 62 is associated with
each nacelle 11 and 19 so as to provide a three-point landing gear
system. Alternatively, as shown in FIGS. 9, 10, and 11, a trunk 62a
may be associated with the leading and trailing edges 20a and 22a
of each wing 18a. To this end, a trunk 62a is configured to the
wing planform extending across the center nacelle 11a and chordwise
of the wing 18a at each outer tip, i.e., outer nacelles 19a. Thus,
when the trunk 62a is inflated by bleed air from the engine fan
exhaust through the spanwise ducts 35 and conduits 35', the
distance between the holes 63a therein defines an air cushion area
Aa under substantially the entire area of the wings 18a when in
ground effect. When the aircraft 10 is airborne, this trunk 62a
serves to provide a cambered airfoil profile to provide effective
lift augmentation. During flight, the trunk 62a is deflated and
draws taut against the associated wing surface for minimum
drag.
Referring specifically now to FIG. 8, a means for augmenting the
lateral and directional control moments of the aircraft 10 is
illustrated. The movable surface 64 represents either the rudder or
elevator, as the case may be, hinged in any conventional manner
about a pivot axis 65 to stationary empennage structure (either the
vertical stabilizer 24 or the horizontal stabilizer 25). An
extension duct 66 is connected to the air duct 35 at the outer end
thereof, being disposed within the vertical stabilizer 24 and
terminating adjacent the outer end tips of the horizontal
stabilizer 25. Compressed air passing through the duct 66 is guided
to the exterior surfaces of the movable member 64 through channels
67 terminating at the slotted nozzles 68.
When the movable member 64 is located in the neutral position, as
indicated by solid lines, the slotted nozzles 68 are closed by
contact with the arcuate surfaces 69, described about the pivot
axis 65. When the member 64 is displaced in either direction, for
example downward as shown in broken lines, the upper slotted
nozzles 68 are opened due to the flat surface 70. At the same time
the lower slotted nozzles 68 remain closed due to continued contact
with the associated arcuate surface 69. Thus, compressed air in the
duct 66 is discharged through the slotted nozzles 68 on either side
of the member 64 to effect the attached flow of the free air due to
removal of the boundary layer thereon.
* * * * *